IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v205y2023icp291-314.html
   My bibliography  Save this article

Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

Author

Listed:
  • Hoang, Manh Tuan

Abstract

The aim of this work is to study qualitative dynamical properties of a generalized hepatitis B epidemic model and its dynamically consistent discrete model. Positivity, boundedness, the basic reproduction number and asymptotic stability properties of the model are analyzed rigorously. By the Lyapunov stability theory and the Poincare–Bendixson theorem in combination with the Bendixson–Dulac criterion, we show that a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number R0≤1 and a disease-endemic equilibrium point is globally asymptotically stable whenever R0>1. Next, we apply the Mickens’ methodology to propose a dynamically consistent nonstandard finite difference (NSFD) scheme for the continuous model. By rigorous mathematical analysis, it is proved that the constructed NSFD scheme preserves essential mathematical features of the continuous model for all finite step sizes. Finally, numerical experiments are conducted to illustrate the theoretical findings and to demonstrate advantages of the NSFD scheme over standard ones. The obtained results in this work not only improve but also generalize some existing recognized works.

Suggested Citation

  • Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:291-314
    DOI: 10.1016/j.matcom.2022.10.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422004074
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.10.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Khan, Tahir & Khan, Amir & Zaman, Gul, 2018. "The extinction and persistence of the stochastic hepatitis B epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 123-128.
    2. Danane, Jaouad & Allali, Karam & Hammouch, Zakia, 2020. "Mathematical analysis of a fractional differential model of HBV infection with antibody immune response," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Gao, Fei & Li, Xiling & Li, Wenqin & Zhou, Xianjin, 2021. "Stability analysis of a fractional-order novel hepatitis B virus model with immune delay based on Caputo-Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Garba, S.M. & Gumel, A.B. & Hassan, A.S. & Lubuma, J.M.-S., 2015. "Switching from exact scheme to nonstandard finite difference scheme for linear delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 388-403.
    5. Hoang, Manh Tuan, 2022. "Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 32-56.
    6. Tuan Hoang, Manh & Nagy, A.M., 2019. "Uniform asymptotic stability of a Logistic model with feedback control of fractional order and nonstandard finite difference schemes," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 24-34.
    7. Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "On the analysis of semi-analytical solutions of Hepatitis B epidemic model under the Caputo-Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Wood, Daniel T. & Kojouharov, Hristo V. & Dimitrov, Dobromir T., 2017. "Universal approaches to approximate biological systems with nonstandard finite difference methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 337-350.
    9. Arenas, Abraham J. & González-Parra, Gilberto & Chen-Charpentier, Benito M., 2016. "Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 48-63.
    10. Cardoso, Lislaine Cristina & Camargo, Rubens Figueiredo & dos Santos, Fernando Luiz Pio & Dos Santos, José Paulo Carvalho, 2021. "Global stability analysis of a fractional differential system in hepatitis B," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    11. Khan, Tahir & Ullah, Zakir & Ali, Nigar & Zaman, Gul, 2019. "Modeling and control of the hepatitis B virus spreading using an epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 1-9.
    12. Shah, Syed Azhar Ali & Khan, Muhammad Altaf & Farooq, Muhammad & Ullah, Saif & Alzahrani, Ebraheem O., 2020. "A fractional order model for Hepatitis B virus with treatment via Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    13. Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Carlos Julio Mayorga & María Ángeles Castro & Antonio Sirvent & Francisco Rodríguez, 2023. "On the Construction of Exact Numerical Schemes for Linear Delay Models," Mathematics, MDPI, vol. 11(8), pages 1-9, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hoang, Manh Tuan, 2022. "Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 32-56.
    2. Hoang, Manh Tuan, 2022. "Positivity and boundedness preserving nonstandard finite difference schemes for solving Volterra’s population growth model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 359-373.
    3. Tingting Xue & Xiaolin Fan & Yan Xu, 2023. "Kinetic Behavior and Optimal Control of a Fractional-Order Hepatitis B Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
    4. Yaagoub, Zakaria & Allali, Karam, 2022. "Fractional HBV infection model with both cell-to-cell and virus-to-cell transmissions and adaptive immunity," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    5. Li, Xiao-Ping & Din, Anwarud & Zeb, Anwar & Kumar, Sunil & Saeed, Tareq, 2022. "The impact of Lévy noise on a stochastic and fractal-fractional Atangana–Baleanu order hepatitis B model under real statistical data," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    6. Carlos Julio Mayorga & María Ángeles Castro & Antonio Sirvent & Francisco Rodríguez, 2023. "On the Construction of Exact Numerical Schemes for Linear Delay Models," Mathematics, MDPI, vol. 11(8), pages 1-9, April.
    7. Mohamed M. Mousa & Fahad Alsharari, 2021. "A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases," Mathematics, MDPI, vol. 9(22), pages 1-12, November.
    8. Sunil Kumar & Ali Ahmadian & Ranbir Kumar & Devendra Kumar & Jagdev Singh & Dumitru Baleanu & Mehdi Salimi, 2020. "An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets," Mathematics, MDPI, vol. 8(4), pages 1-22, April.
    9. Fatima, Bibi & Zaman, Gul, 2020. "Co-infection of Middle Eastern respiratory syndrome coronavirus and pulmonary tuberculosis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2022. "Ergodic stationary distribution of stochastic epidemic model for HBV with double saturated incidence rates and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    11. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    12. Ghanbari, Behzad, 2021. "On detecting chaos in a prey-predator model with prey’s counter-attack on juvenile predators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    13. García, M.A. & Castro, M.A. & Martín, J.A. & Rodríguez, F., 2018. "Exact and nonstandard numerical schemes for linear delay differential models," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 337-345.
    14. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 41-49.
    15. Amiri, Pari & Afshari, Hojjat, 2022. "Common fixed point results for multi-valued mappings in complex-valued double controlled metric spaces and their applications to the existence of solution of fractional integral inclusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    16. Attia, Nourhane & Akgül, Ali & Seba, Djamila & Nour, Abdelkader, 2020. "An efficient numerical technique for a biological population model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    17. Iqbal, Zafar & Ahmed, Nauman & Baleanu, Dumitru & Adel, Waleed & Rafiq, Muhammad & Aziz-ur Rehman, Muhammad & Alshomrani, Ali Saleh, 2020. "Positivity and boundedness preserving numerical algorithm for the solution of fractional nonlinear epidemic model of HIV/AIDS transmission," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    18. Pasha, Syed Ahmed & Nawaz, Yasir & Arif, Muhammad Shoaib, 2023. "On the nonstandard finite difference method for reaction–diffusion models," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    19. Du, Feifei & Lu, Jun-Guo, 2021. "New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    20. Shah, Kamal & Abdeljawad, Thabet & Ud Din, Rahim, 2022. "To study the transmission dynamic of SARS-CoV-2 using nonlinear saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:291-314. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.